Swaying after hitting dips/bumps 50MPH +

I purchased a 2000 LS a few days ago from a dealer auction and have sorted out the coil problem and put 4 brand new tires and a had a 4 point alignment done on it as well but I noticed on the highway the other day I was running around 65MPH when I hit a dip in the road the car felt like it was swaying to the point the hair on the back of my neck stood up it was very scary. It feels like the car is going straight and the steering is fine around corners but as soon as I hit a dip or pot whole the car feels like its going one way and I'm going another so Is there any advice on what could be the possible cause of this before I take it to the dealer for diagnostics? I usually work on vehicles myself but this seems to be something more on the lines of a professional. I checked the lug nuts and made sure the wheels where tight when I wiggled them and have also checked the steering column for any play and that turned out fine as well. I also have a slight crunch in the front in when going slowly over speeds bumps as well. I did make a call to the service dept at lincoln and the guy said it sounded like the tires but like I mentioned above they are brand spankin new and have les than 500 miles on them. Thanks in advanced for any insight.

Did you notice this before putting the new tires on it and got the alignment? You may want to try rotating the tires front to rear to see if the "bump steering" changes.

-Rod

Did you notice this before putting the new tires on it and got the alignment? You may want to try rotating the tires front to rear to see if the "bump steering" changes.

-Rod

Well i never noticed this before the new tires because i never took her o the highway the auction I got the car from is only a few miles from my house as well as the tire shop I took it to. I will try and rotate the tires when I have the time to see if that inhibits any changes. The car feels rock sturdy around corners and normal driving on regular roads its just when she is going past 50 on the highway and hits a dip it feels like the car is sliding without actually sliding of course, its just kinda hard to explain I guess. Anyhow I do appreciate the feedback and really love driving the car just not on the interstate right now. I did happen to notice the tires that got put on the car look a bit small for the car 215/60/R16 95H not sure if that would make it do as described in the above.